This thesis is aimed at analysis of sampled-data feedback systems. Our approach is in the frequency-domain, and stresses the study of sensitivity and complementary sensitivity operators. Frequency-domain methods have proven very successful in the analysis and design of linear time-invariant control systems, for which the importance and utility of sensitivity operators is well-recognized. The extension of these methods to sampled-data systems, however, is not straightforward, since they are inherently time-varying due to the intrinsic sample and hold operations. In this thesis we present a systematic frequency-domain framework to describe sampled-data systems considering full-time information. Using this framework, we develop a theory of design limitations for sampled-data systems. This theory allows us to quantify the essential constraints in design imposed by inherent open-loop characteristics of the analog plant. Our results show that: (i) sampled-data systems inherit the difficulty imposed upon analog feedback design by the plant's non-minimum phase zeros, unstable poles, and time-delays, independently of the type of hold used; (ii) sampled-data systems are subject to additional design limitations imposed by potential non-minimum phase zeros of the hold device; and (iii) sampled-data systems, unlike analog systems, are subject to limits upon the ability of high compensator gain to achieve disturbance rejection. As an application, we quantitatively analyze the sensitivity and robustness characteristics of digital control schemes that rely on the use of generalized sampled-data hold functions, whose frequency-response properties we describe in detail. In addition, we derive closed-form expressions to compute the L2-induced norms of the sampled-data sensitivity and complementary sensitivity operators. These expressions are important both in analysis and design, particularly when uncertainty in the model of the plant is considered. Our methods provide some interesting interpretations in terms of signal spaces, and admit straightforward implementation in a numerically reliable fashion.